Angular and Linear Momentum in General Relativity: Their Geometric Structure and Interrelation

TL;DR

This paper introduces generalized, geometrically meaningful definitions of angular and linear momentum in general relativity, connecting them to classical notions and illustrating their properties with the boosted Schwarzschild solution.

Contribution

It provides new geometric definitions of momentum in general relativity that unify and extend previous concepts, clarifying their interrelation and physical significance.

Findings

Definitions reduce to ADM and null infinity limits

Expresses angular momentum in terms of linear momentum

Illustrates concepts with boosted Schwarzschild solution

Abstract

Generalized definitions for angular and linear momentum are given and shown to reduce to the ADM (at spatial infinity) definitions and the definitions at null infinity in the appropriate limit. These definitions are used to express angular momentum in terms of linear momentum. The formalism allows one to see the connection with the classical and special relativitistic notions of momenta. Further, the techniques elucidate, for the first time, the geometric nature of these conserved quantities. The boosted Schwarzschild solution is used to illustrate some aspects. The definitions are useful and give insight in the region far from all masses where gravity waves are detected.